In this section, we evaluate the performance of our method in point cloud learning tasks including object classification, object part segmentation, and indoor scene segmentation. For parameter settings, our network has a total of four PVC layers. From the first to the last layer, grid size is set to \(G_0 = 32, G_1=16, G_2=8, G_3=4\)  respectively. Number of neighbors for KNN search is 32. Dilation step is \(n_0=1, n_1=2, n_2=4, n_3=8\) . Our method is implemented with PyTorch [1]} and run on a Nvidia TitanXP GPU.
Batch size for training is set to be 16. We use the Adam optimizer [2]} with default settings. The learning rate is initialized as 0.001 and decays by a rate of 0.5 every 20 epochs. Object classification converges around 100 epochs, part segmentation converges at 80 epochs, and indoor scene segmentation converges at 120 epochs. The full version of our network has \(C=64\)  feature channels for the first PVC layer. Feature channel for l-th layer is \(C\times 2^{l-1}\) .
